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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 3, 2000, pp. 847–852
DOI: 10.4171/ZAA/983

Published online: 2000-09-30

On the Existence of $C^1$ Functions with Perfect Level Sets

Emma D'Aniello[1] and U.B. Darji[2]

(1) Università degli Studi di Napoli, Caserta, Italy
(2) University of Louisville, USA

Given a closed set $M \subset [0, 1]$ of Lebesgue measure zero, we construct a $C^1$ function $f$ with the property that $f^{–1} ({y})$ is a perfect set for every $y$ in $M$.

Keywords: Level sets, $C^1$ functions

D'Aniello Emma, Darji U.B.: On the Existence of $C^1$ Functions with Perfect Level Sets. Z. Anal. Anwend. 19 (2000), 847-852. doi: 10.4171/ZAA/983